The Republican presidential nominee went on to praise Israel's policing practices. Israeli security forces routinely conduct general roundups for questioning or during specific investigations.
"You know in Israel, they profile," Trump said. "They've done an unbelievable job — as good as you can do. But Israel has done an unbelievable job. And they'll profile. They profile. They see somebody that's suspicious. They will profile. They will take that person in. They will check out."
Trump concluded: "Do we have a choice? Look what's going on. Do we really have a choice? We're tying to be so politically correct in our country."
It's not the first time Trump has made a suggestion that racial profiling could be an effective tactic.
"But look, we have — whether it's racial profiling or politically correct, we'd better get smart," he said at a Fox News town hall in August. "We are letting tens of thousands of people into our country. We don't know what the hell we're doing."
Trump said he is "totally in favor of freedom of the press," but that authorities should "arrest" people who are publishing information in magazines and on web sites about how to make bombs.
On Saturday night, as initial reports about an explosion in Manhattan were still coming in and before the authorities had announced the details, Trump told supporters at a rally that a "bomb" had gone off in New York. On Monday, he bragged about his choice of words.
"What I said is exactly correct. I should be a newscaster because I called it before the news," Trump said.
"I must tell you that just before I got off the plane, a bomb went off in New York and nobody knows exactly what's going on," Trump said shortly after he deplaned at a rally in Colorado Springs on Saturday night.
The New York Police Department said Monday that it is seeking 28-year-old Ahmad Khan Rahami, a naturalized U.S. citizen born in Afghanistan, in connection with Saturday’s bombing in Manhattan. It was not clear what his role in the incident is thought to be.
Trump offered a highly vague strategy for combating the Islamic State and other terrorists overseas, saying we have to "knock the hell out of 'em." He repeated his criticism of President Obama and Democratic presidential nominee Hillary Clinton, blaming them for allowing too many Syrian refugees into the country.
The discussion focused heavily on the bombing in New York and recent stabbing in a Minnesota mall. A news agency linked to the Islamic State claimed that the Minnesota attacker was “a soldier of the Islamic State.”
"Maybe we're going to be seeing a big change over the last couple of days. I think this is something that maybe will get, you know, will happen perhaps more and more over the country," Trump warned.
A campaign official confirmed Monday that Trump plans to meet with Egyptian President Abdel Fattah el-Sisi this evening.
Trump also predicted he would be treated "very unfairly" at the upcoming presidential debate, on Sept. 26. He said that he has always found NBC's Lester Holt, who is slated to moderate the first debate, "to be fair," but that the process is a "very, very dirty system."